Journal ArticleDOI
Indentation size effects in crystalline materials: A law for strain gradient plasticity
William D. Nix,Huajian Gao +1 more
TLDR
In this article, the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations, which leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H 0 is a characteristic length that depends on the shape of the indenter, the shear modulus and H 0.Abstract:
We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness: H H 0 1+ h ∗ h where H is the hardness for a given depth of indentation, h, H0 is the hardness in the limit of infinite depth and h ∗ is a characteristic length that depends on the shape of the indenter, the shear modulus and H0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver. We use this model to derive the following law for strain gradient plasticity: ( σ σ 0 ) 2 = 1 + l χ , where σ is the effective flow stress in the presence of a gradient, σ0 is the flow stress in the absence of a gradient, χ is the effective strain gradient and l a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient, l ≈ b( μ σ 0 ) 2 . For materials characterized by the power law σ 0 = σ ref e 1 n , the above law can be recast in a form with a strain-independent material length scale l. ( builtσ σ ref ) 2 = e 2 n + l χ l = b( μ σ ref ) 2 = l ( σ 0 σ ref ) 2 . This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parametersbl].read more
Citations
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Scale effects in dry and wet friction, wear, and interface temperature
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Fracture in a higher-order elastic continuum
TL;DR: In this paper, the authors obtained analytically the mode I and mode II full-field solutions for a semi-infinite crack in an infinite solid characterized by the higher-order elastic continuum theory.
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Effect of indenter size on elastic modulus of cartilage measured by indentation.
TL;DR: The equilibrium elastic modulus of bovine patellar cartilage measured by indentation depends on tip size, which appears to be an inherent feature of indentation of cartilage, perhaps due to its inhomogeneous structure.
Journal ArticleDOI
A mechanistic model for depth-dependent hardness of ion irradiated metals
TL;DR: In this article, a mechanistic model was developed for modeling the depth-dependent hardness in ion irradiated metallic materials, which is capable of capturing the indentation size effect, ion irradiation induced damage gradient effect, and effect of unirradiated region acting as a soft substrate.
Journal ArticleDOI
TEM, XRD and nanoindentation characterization of Xenon ion irradiation damage in austenitic stainless steels
TL;DR: In this paper, a 20% cold-worked 316 austenitic stainless steel (CW 316 SS) has been characterized by TEM, XRD and nanoindentation to determine the microstructural evolution and mechanical property changes of 316 SS after irradiation with 7 MeV Xe26+ ions.
References
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Journal ArticleDOI
The deformation of plastically non-homogeneous materials
TL;DR: The geometrically necessary dislocations as discussed by the authors were introduced to distinguish them from the statistically storages in pure crystals during straining and are responsible for the normal 3-stage hardening.
Journal ArticleDOI
Strain gradient plasticity: Theory and experiment
TL;DR: In this paper, a deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening, which is a non-linear generalization of Cosserat couple stress theory.
Journal ArticleDOI
A phenomenological theory for strain gradient effects in plasticity
TL;DR: In this paper, a strain gradient theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations, which fits within the general framework of couple stress theory and involves a single material length scale l.
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